Contradiction with 2 Samuel 6:6-7
This verse describes how Uzzah was struck dead for touching the Ark, whereas 1 Chronicles 13:13 mentions the Ark being safely kept at the house of Obed-edom, showing differing fates for those handling the Ark.
2 Samuel 6:6-7: And when they came to Nachon's threshingfloor, Uzzah put forth [his hand] to the ark of God, and took hold of it; for the oxen shook [it]. [Nachon: also called Chidon] [shook it: or, stumbled]
Contradiction with 1 Kings 8:6-11
This passage details the Ark being successfully moved into the Temple by Solomon, in contrast to 1 Chronicles 13:13, where David decides not to move the Ark to Jerusalem.
1 Kings 8:6-11: And the priests brought in the ark of the covenant of the LORD unto his place, into the oracle of the house, to the most holy [place, even] under the wings of the cherubims.
Contradiction with 1 Chronicles 15:25-28
This passage describes the successful transportation of the Ark to Jerusalem unlike 1 Chronicles 13:13, where the Ark remains at Obed-edom's house.
1 Chronicles 15:25-28: So David, and the elders of Israel, and the captains over thousands, went to bring up the ark of the covenant of the LORD out of the house of Obededom with joy.